There used to be a "Download" option as you navigated to each of your albums on Photobucket, but I don't see that option anymore. I wonder if Photobucket removed that option just so they can be even bigger [censored] to people.

It is possible using their website, although I do not recall the exact steps how. My dad is in a similar situation to everyone else, trying to retrieve his photos from a service that is no longer free. We found out how to do it, but the site, so overloaded with others trying to do the same, was unresponsive and we were unsuccessful while I was there.